A333246 Number of self-avoiding closed paths on an n X n grid which pass through NW corner.

1, 7, 97, 4111, 532269, 212372937, 263708907211, 1013068026356375, 11955420069208095719, 432101605951906251627393, 47778407166747833830058004149, 16149888968763663448192636077980753, 16675786862526496319891707194153887550751, 52568166380872328447478940416604864445574575709

Offset: 2

Author

Seiichi Manyama, Mar 23 2020

Keywords

• nonn

Examples

			a(2) = 1;
   +--*
   |  |
   *--*
a(3) = 7;
   +--*      +--*--*   +--*--*   +--*
   |  |      |     |   |     |   |  |
   *--*      *--*--*   *     *   *  *
                       |     |   |  |
                       *--*--*   *--*
   +--*--*   +--*--*   +--*
   |     |   |     |   |  |
   *  *--*   *--*  *   *  *--*
   |  |         |  |   |     |
   *--*         *--*   *--*--*
		

Crossrefs

Cf. A140517, A333247, A333323, A333438, A333439, A333466.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A333246(n):
    universe = tl.grid(n - 1, n - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles().including(1)
    return cycles.len()
print([A333246(n) for n in range(2, 10)])

Formula

a(n) = A333439(n) - 1 for n > 1.

Extensions

a(11), a(13) from Seiichi Manyama, Apr 07 2020

a(10), a(12), a(14)-a(15) from Andrew Howroyd, Jan 30 2022